A birth ball is simply an exercise ball that helps in pregnancy & labour.
In pregnancy it helps to strengthen your back and better support the pelvis to establish balance. It's good to sit with your knees slightly lower than your hips so your in an anterior position with the pelvis. You an then make figure 8, circles, rocking and swaying movements to open the inlet of your pelvis so your baby can engage in the last weeks of your pregnancy.
In labour you can help your baby rotate from the posterior position by doing lots of circling and figure 8 and rocking. You can also use circling on the ball to increase the strength of contractions after a rupture of membranes ie. helping the baby bring their head on to the cervix more.
I have had midwives report that when the mother is on the ball and breathing slowly that the baby's heart rate is good and that the breathing and upright positions are great way for her to relax. Do ball rolling for 20 mins and then walk around or rest.